Not sure having to fight wild animal and possible skirmishes with other tribes was much better than war, nor that having the regular infection and illness was in any way different for the regular guy than plague.
Being eaten by a bear isn't much better than being disemboweled by a Viking, no doubt, and dying of a gangrenous limb isn't evidently preferable to dying of the pox.
But, the question is not the gnarliness of the death, it's the likelihood of any given human encountering such an end. Fighting a wild animal is something that happens rarely, for a brief moment of time, and in very specific contexts. It's fairly rare for animals to attack humans, and humans would only hunt dangerous animals like bears or boars in certain circumstances. Similarly, while untreatable infections may occur, they would largely result from severe and infrequent accidents. These are things which people have at least a degree of control over, and a careful man could survive until at least middle age without either threatening his life.
War and plague are very different propositions. They occur all at once, to everyone. Armies sweep across landscapes, burning homes, ravaging fields, uprooting communities that may have existed for generations. Plagues infect entire communities, exterminating generations and collapsing agricultural systems. The Black Death killed every third person in Europe; the Thirty Years War killed every second person in Germany. Whether or not a given individual encountered such threats had little to do with individual choices, but to great, impersonal forces beyond their control.
And the thing is, the above isn't speculative. We have records, mostly-second hand but a few first-hand, of people who live in simple, dispersed societies encountering the civilised threats of war and famine, and being consciously aware that this is some new and terrible.
The rousseauist view of our ancestors being peace loving pacifists and that the ills of the world are due to agrarian society is not really true either.
It's super-weird to me that any discussion this stuff has to begin with a ritualised consideration of and distancing from Hobbes and Rousseau, as if there was any other context in which the opinions of two specific but extremely dead men were assumed to wield that level of continuing authority.
Large scale war certainly is an invention of the post agrarian revolution world, but mostly because before that the population levels were so small that you didn't have polities large enough to recruit hundreds or thousands of men to have war, with a capital W, with the Other on a battlefield over their land, ladies and loot. A war or a genocide in the paleolithic/mesolithic didn't involve killing thousands of people, because there weren't many people to kill anyway. Killing 20 people could push your competing tribe to the brink of extinction by forcing them to leave their subsistence area, and fleeing to an are inhibited by another tribe.
I think it's a bit simplistic to treat this as a simple question of scale, as if it was materially possible for a tribe of one hundred and a nation of one million to wage war in the same fashion. Small, decentralised societies don't have the resources to wage extended or intensive wars, not least because their most valuable resource, human beings, is one that wars tend to burn through pretty quickly. Large-scale extended warfare requires either a dedicated warrior-class or classes who are economically marginal-enough that a society can afford to have them off fighting for months or years at a time, or it requires a powerful centralised state that can draft large parts of the working population without collapsing the economy. In simple societies, warfare is necessarily limited to ritualised confrontations or to one-off raids; there simply isn't the material basis for extended campaigns, not unless some powerful outside empire is prepared to subsidise them.
Wiping out a dozen people may decimate a tribe, but it's also much easier said than done. While it's certainly probably that there were some extremely violent encounters in simple societies, there's not a lot of evidence to suggest that they occurred on even a relative scale with the frequency they do in the "civilised" age.
